Question

Four students reported their study time and test score from a statistics course and their data have been converted into Z scores in the table below. What is Pearson's correlation coefficient from this data set?

Group of answer choices

a.)-.50

b.)-.25

c.).75

d.)-1.00

In what situation would a researcher use a  t-test used instead of a Z-test?

Group of answer choices

a.)When there is only one sample.

b.)When the population standard deviation is unknown.

c.)When the sample size is smaller than 30.

d.)When the population is normally distributed.

If you conduct a two-tailed test at the .05 level of significance, with a degree of freedom of 30, what would be your critical t score on the t distribution?

a.)±2.043

b.)±1.729

c.)2.043

d.)1.729

A researcher tested a research hypothesis that people with diagnosed depression will have REDUCED level of depressive symptoms after a cognitive therapy treatment, as compared to the pre-treatment level of depressive symptoms. The cutoff t value is -1.746 for this one-tailed test. The data analysis yielded a mean change score (post-treatment minus pre-treatment) of -3. If the standard error is 2.0, what is the t statistic and what is the conclusion of the hypothesis test?

Group of answer choices

a.)-1.50; fail to reject the null hypothesis

b.)-1.50; reject the null hypothesis

c.)-1.25; fail to reject the null hypothesis

d.)-1.25; reject the null hypothesis

Answer 1

1)Since study time and test scores are directly related to each other ( as study time increases test scores also increase) the correlation coefficient will be positive value.

r = 0.75

Negative scores indicate inverse relationship.

2) t test and z assume that population should be normally distributed and both can be used to test single population mean .

Z test assumes that population standard deviation is known.

Correct option : when population standard deviation is unknown.

3) critical value of t for two sided test at df 30 is equal to +- 2.043. When test is two sided it's critical region is equally divided on two sides of distribution. Therefore there are two critical values . Positive critical values are only for right tailed test.

4) t = mean change score/ standard Error

t = -3/2 = - 1.5

| - 1.746 | > | -1.5 | , we fail to Reject Null hypothesis.